Find four angles in different quadrants with the reference angle $15^{\circ}$. Enter your answers for $0^{\circ} \leq \theta \leq 360^{\circ}$ in increasing order.
Answer
Final Answer: The four angles in different quadrants with the reference angle \(15^{\circ}\) are \(\boxed{15^{\circ}, 165^{\circ}, 195^{\circ}, 345^{\circ}}\).
Step 1 ：Define the reference angle as \(15^{\circ}\).
Step 2 ：In the first quadrant, the angle is just the reference angle itself, which is \(15^{\circ}\).
Step 3 ：In the second quadrant, the angle is \(180^{\circ} - 15^{\circ} = 165^{\circ}\).
Step 4 ：In the third quadrant, the angle is \(180^{\circ} + 15^{\circ} = 195^{\circ}\).
Step 5 ：In the fourth quadrant, the angle is \(360^{\circ} - 15^{\circ} = 345^{\circ}\).
Step 6 ：Final Answer: The four angles in different quadrants with the reference angle \(15^{\circ}\) are \(\boxed{15^{\circ}, 165^{\circ}, 195^{\circ}, 345^{\circ}}\).
